CN-121982143-A - Electromagnetic backscatter robust imaging method based on maximum correlation entropy and subspace optimization fusion

Abstract

The invention discloses an electromagnetic backscatter robust imaging method based on optimal fusion of maximum correlation entropy and subspace. The method decomposes a contrast source into deterministic/ambiguous subspaces under an SOM framework, constructs a data-state dual-channel robust cost function through MCC, and converts non-convex optimization into a sequence weighted quadratic sub-problem based on Half Quadratic (HQ) and IRLS. And (3) adaptively inhibiting outliers through Gaussian kernel weights, and updating closed weighting solutions of the manifold subspace coefficients and the contrast by adopting an alternating strategy to realize effective inhibition of pulse, heavy tail and speckle noise. The method is free in training, can be interpreted physically, has rapid convergence and high robustness, and is suitable for high-fidelity inversion in non-Gaussian noise environments such as radar imaging, medical imaging, underground detection and the like.

Inventors

• BI DONGJIE
• LI XIFENG
• ZHANG TINGSEN
• PENG LIBIAO
• Gui Suyao
• XIE YONGLE
• SHUAI PING
• XIE XUAN
• WANG ZHENSONG

Assignees

• 电子科技大学

Dates

Publication Date

20260505

Application Date

20251225

Claims (4)

1. 1. An electromagnetic backscatter robust imaging method based on maximum correlation entropy and subspace optimization fusion, the method comprising: step 1, establishing a discretization operator model of an electromagnetic scattering problem; discretizing the region D of the target to be inverted into N grid units, and on the basis, discretizing the state equation and the data equation to obtain an operator model in the form of the following matrix: discrete state equation describing the total field inside the scattering region D From incident field And a contrast source The generated fields are superimposed as shown in formula 1: (1); Discrete data equations describing the measured scattered field at the receiving antenna outside the scattering region Is made up of contrast sources within region D Radiation generated as shown in formula 2: (2); wherein each symbol is defined as follows: a known quantity, which is a vectorized representation of the incident field over N discrete grid cells; a known quantity, a vectorized representation of the fringe field data measured for Nr receive antennas; unknown quantity is vectorized representation of a comparison source to be solved on N discrete grid units; The unknown quantity is the vectorized representation of the target contrast function to be finally solved on N discrete grid cells, the contrast source Contrast with contrast ratio The following relationships are satisfied: (3); Wherein the method comprises the steps of Representing the vector A diagonal matrix is formed; discrete domain green operator, a matrix pre-computed from a discretized grid, for describing interactions between discrete elements within region D, will compare sources Mapping to a fringe field generated within region D; Discrete scattering green operator, a matrix pre-computed from the discretized grid and the receiver antenna positions, for describing the field propagation of the source in region D to the external receiver antenna, will compare the source Mapping to a fringe field generated at the receiving antenna; Step 2, subspace decomposition and deterministic/ambiguous component initialization based on SVD; for discrete scattering green operator Singular value decomposition: (4); Wherein the method comprises the steps of And Is unitary matrix with column vector And Respectively left singular vector and right singular vector, diagonal matrix Comprising real non-negative singular values arranged in non-increasing order Right singular vector set Forming contrast source space Is a complete orthogonal basis for (a) the (c), From the following components The composition of the composite material comprises the components, From the following components Composition; selecting a cutoff threshold L, the basis being divided into two orthogonally complementary subspaces, determining a sex subspace And ambiguous subspaces Determining the sex subspace from the first L right singular vectors Tensed, these vectors correspond to singular values above a certain noise correlation threshold, representing components of the contrast source that are of high radiation intensity and that can be well captured by the receiver, the ambiguous subspace being formed by the remaining N-L right singular vectors Tensed, representing a weakly radiating or non-radiating source component; incident field for the ith emitter Corresponding contrast source Projected onto the two subspaces to obtain a deterministic portion And ambiguous part Wherein By applying to scattered field data Is obtained by non-iterative solution of truncated pseudo-inverse of (5) and ambiguous part Is positioned in the noise subspace, cannot be determined only by a data equation, and is a linear combination of the basis vectors of the noise subspace, as shown in the formula 6; (5); (6); Wherein the method comprises the steps of Is a coefficient vector to be estimated; Step3, constructing a two-channel cost function based on a maximum correlation entropy criterion; the electromagnetic backscatter inversion problem in the above steps is reduced to find contrast distribution Sum coefficient vector set Restating the data into an optimization problem, wherein the cost function J MCC is formed by a data fidelity item and a state fidelity item, and the two fidelity items are measured based on a maximum related entropy criterion; Step 4, performing equivalent transformation on the cost function and establishing an iteration weighted least square frame; step 5, alternately iterating and optimizing the solution; In the (k+1) th iteration, an alternating optimization strategy is adopted, one variable is fixed, the optimal solution of the other variable is solved, and the weight and the fuzzy source coefficient are updated sequentially And contrast distribution ; Step 6, convergence judgment and result output; Repeatedly executing the alternate iteration process of the step 5 until the preset convergence condition is met, and outputting the finally obtained contrast function after the iteration is ended And obtaining the electromagnetic parameter spatial distribution reconstruction result of the target.
2. 2. The electromagnetic backscatter robust imaging method based on maximum correlation entropy and subspace optimization fusion of claim 1, wherein the specific method of step 3 is: Defining the data residual error corresponding to the ith incident wave to be obtained by the current contrast source Generated calculated fringe field And actually measuring the scattered field The difference value is shown in the formula 7, and the state residual error corresponding to the ith incident wave is defined by the current contrast source With current contrast The difference between the contrast source calculated from the incident field is shown in equation 8; (7); (8); for residual vectors The cost function based on the correlation entropy uses a gaussian kernel Construction aimed at maximizing This is mathematically equivalent to minimizing the following objective function: (9); by applying a gaussian kernel to these residuals and summing all transmitters and spatial locations, the objective function is: (10); Wherein N i is the total number of transmitting antennas, >0 Is a regularization parameter used to balance data and state fidelity terms, while And >0 is the kernel width for controlling the robustness of the estimator, smaller values will yield stronger outlier rejection, larger values will approach the minimum mean square error.
3. 3. The electromagnetic backscatter robust imaging method based on maximum correlation entropy and subspace optimization fusion of claim 1, wherein the specific method of step 4 is as follows: defining a weight for each residual term as shown in equations 11, 12; (11); (12); minimization of Equivalent minimizes the proxy objective function that is a quadratic function with respect to its variables while the other variables remain unchanged: (13); Wherein the method comprises the steps of And Is a diagonal weight matrix; representing the two weights established.
4. 4. The electromagnetic backscatter robust imaging method based on maximum correlation entropy and subspace optimization fusion of claim 1, wherein the specific method of step 5 is that step 5.1 is that the weight is updated The superscript k indicates the corresponding number of iterations, using the last iteration And Calculating residual errors And As shown below; (14); (15); then calculate the weight matrix of all the incident waves And ; Step 5.2 updating the fuzzy source coefficient Fixing means And weight Minimizing Is a function of (2) Is provided with A kind of electronic device The weighted form of the ith incident wave is: (16); Thereby obtaining Is a linear system of equations: (17); solving the formula (17) by a conjugate gradient method; Step 5.3 updating contrast function Fixed fuzzy source coefficient And weight Total contrast source And total field Calculated from the following formula: (18); (19); For each spatial element n, about Is the objective function of (2) Is minimized in (a) is decoupled; thereby obtaining each element Is a closed form solution of: (20)。

Description

Electromagnetic backscatter robust imaging method based on maximum correlation entropy and subspace optimization fusion Technical Field The invention belongs to the field of Electromagnetic wave imaging and signal processing, and particularly relates to an imaging reconstruction method for an Electromagnetic INVERSE SCATTERING Proglems (EISPs) problem, in particular to a reconstruction method with high robustness and high precision in a non-Gaussian noise environment. Background The electromagnetic backscattering technology aims at inverting the spatial distribution of electromagnetic physical parameters (such as dielectric constant and conductivity) inside the target by measuring electromagnetic field data after the scattering of the target. The technology has important application value in the fields of radar imaging, medical diagnosis, geophysical exploration, nondestructive detection and the like. The theoretical basis is Lippmann-Schwinger type integral equation expressed by Maxwell's equation set and green's function. The model is expressed as multiplication coupling of medium contrast and total field and nonlinear superposition of multiple scattering items in a continuous domain, and after discretization, the corresponding compact high-dimensional operator mapping is performed, and singular value spectrums are rapidly attenuated, so that separation of signals and noise subspaces is not stable, and any tiny observation disturbance can be amplified in inverse mapping to form typical discomfort. The engineering system has the common problems of limited aperture, limited frequency bandwidth and non-uniform array layout, further causes the interception of angular spectrum and spatial frequency domain, thereby weakening the observability of a weak radiation mode and a non-radiation mode, bringing about invisible edges, resolution degradation, azimuth dependent artifacts and the like. Meanwhile, model mismatch caused by forward model simplification (such as boundary condition approximation, lattice point discrete error and green function truncation) can be iteratively amplified on a state constraint link, and becomes a hidden source for influencing convergence stability and physical consistency. Existing mainstream reconstruction algorithms, such as contrast source inversion, subspace optimization methods and variant derivative algorithms thereof, are mostly based on minimum Mean Square Error (MSE) as optimization targets. The MSE criterion is mathematically equivalent to assuming that the noise follows a gaussian distribution, which is sensitive to the second moment of the noise. When abnormal values (outliers, generated by non-Gaussian noise) with larger energy exist in the data, the abnormal values can take the dominant role in the optimization process, so that the algorithm misunderstands the noise into a real scattering phenomenon, an incorrect physical model is generated, and finally, the reconstruction result is severely distorted, artifacts and even can not be converged into a physically meaningful solution. Therefore, a novel electromagnetic backscattering method capable of effectively suppressing non-gaussian noise and improving imaging stability and accuracy in a complex electromagnetic environment is needed. Disclosure of Invention The invention provides a backscattering robust imaging method (MCC-SOM) of maximum correlation entropy-subspace optimization fusion, which constructs the correlation entropy cost of a data-state dual-channel by introducing MCC of an information theory into a SOM structure, adopts a semi-quadratic (HQ) and iterative re-weighted least squares (IRLS) framework, and is matched with the alternate updating of deterministic/ambiguous subspaces to realize the self-adaptive suppression of non-Gaussian noise such as pulse, heavy tail, speckle and the like, and simultaneously maintains the efficient convergence and physical interpretability. The invention can obtain high-fidelity reconstruction in various non-Gaussian noise environments without training data and complex network structures, has real-time/quasi-real-time potential and good interpretability, and is suitable for popularization and application in fields with high requirements on safety and reliability, such as medical science, electromagnetic nondestructive detection, underground target detection and the like. The technical scheme of the invention is an electromagnetic backscatter robust imaging method based on optimal fusion of maximum correlation entropy and subspace, which comprises the following steps: step 1, establishing a discretization operator model of an electromagnetic scattering problem; discretizing the region D of the target to be inverted into N grid units, and on the basis, discretizing the state equation and the data equation to obtain an operator model in the form of the following matrix: discrete state equation describing the total field inside the scattering region D From incident fieldAnd a contr